Question: Ben is 2 times as old as Stephanie. Eighteen years ago, Ben was 5 times as old as Stephanie. How old is Stephanie now?
Answer: We can use the given information to write down two equations that describe the ages of Ben and Stephanie. Let Ben's current age be $b$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $b = 2s$ Eighteen years ago, Ben was $b - 18$ years old, and Stephanie was $s - 18$ years old. The information in the second sentence can be expressed in the following equation: $b - 18 = 5(s - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: $b = 2s$ . Substituting this into our second equation, we get: $2s$ $-$ $18 = 5(s - 18)$ which combines the information about $s$ from both of our original equations. Simplifying the right side of this equation, we get: $2 s - 18 = 5 s - 90$ Solving for $s$ , we get: $3 s = 72.$ $s = 24$.